I've been asked a few times what modules I'm running on the drupal installs I'm tending.

Site #1 is domesticat.net, a single-user blog running under 6.x, currently 6.8, with comments enabled.  Site #2 is a firewalled company intranet focused heavily around the concept of using organic groups, has since been written up here.

Modules that are installed but unused because I haven't configured them yet are bolded. Modules that I will turn back on the moment I've got a bugfix are italicized.

I'm undoubtedly missing some fantastic ones, but these are the ones I know about and rely on.

Access and access control

content_access - permits the restriction of access to content based on content type or user role

persistent_login - provides a 'remember me' cookie

tokenauth - provides a unique per-user token, almost always used to provide authenticated RSS feeds that give feedreaders access to content typically only accessible to logged-in users

Anti-spam

mollom - all-in-one anti-spam + intelligent captcha module

spamspan - obfuscates email addresses to prevent spambot harvesting

Comments

ajax_comments - uses AJAX to provide a smoother comment submission process

wp_comments - restructures the comment form into a tighter layout more reminiscent of wordpress

Development-related

coder - helps convert modules from one major version of drupal to another

deadwood - helps convert modules from one major version of drupal to another

drush - command line shell for drupal

Feeds, notifications, and syndication

atom - provides an Atom feed

comment_subscribe - allows users to receive emailed notifications of new comments or replies  (deprecated)
comment_notify - allows users to receive emailed notifications of new comments or replies

commentrss - provides an RSS feed of comments

ljxp - cross-posts to livejournal

mass_contact - sends mass emails to groups of users

service_links - provides links to social sites such as reddit and delicious

pingfm - contacts ping.fm when new content is added

Metadata for my content

onthisday - shows content created on this day in years past.

similarterms - shows list of entries whose terms are similar, and thus probably related

tagadelic - generates a tag cloud

Mobile version of the site

browscap - detects and logs what browsers access your site

mobile_theme - autodetects and presents a slimmed-down theme for mobile browsers

URL structure and navigation

custom_breadcrumbs - defines custom breadcrumb trails for content types

custom_pagers - provides context-sensitive next/previous entries

pathauto - defines custom URL patterns per content type

token - gives access to custom tokens, like creation date, author, title, etc. for many uses, including defining custom URL patterns

User-friendly options

ed_readmore - customizes the "read more" link in posts

fckeditor - WYSIWYG editor

flickr - provides ability to easily embed images from flickr

gravatar - includes gravatars in comments

smileys - automatically turns text smileys into images

colorbox - pretty CSS-based image display code

Utter basics

advanced_help - used to provide extra help in Views

mailhandler - allows post-by-email

sections - allows you to define different themes for certain pages or sections of your site

views - allows you to sort, filter, remix, and present whatever content you want in whatever layout and format you want. (Obscenely powerful.)

xmlsitemap - generates an XML site map for search crawlers.